Episode 145: Pascal’s Wager and Probability Theory

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Speakers are labeled by first name where identified. Unidentified-speaker labels may refer to different people. Bracketed question marks indicate uncertain wording.

Transcript

[00:00:00]  Unidentified speaker: Hello out there.

[00:00:02]  Peter: Today on The Theory of Anything podcast, Bruce takes a deep dive into Pascal's wager. If there is even a small chance that God exists and believing could lead to an infinite reward while disbelief risks an infinite loss, then believing is the rational choice, right? Also, this was completely new to me, but Blaise Pascal is the founder of probability theory all the way back in the 17th century. And even aside from his wager making a potentially problematic theological point, his famous wager also raises issues related to probability theory and Bayes' theorem that came after, and even modern day Bayesian epistemology. How do we handle it when the payoff is large or potentially infinite, in this case, in the form of eternal life? Bruce also hammers home the compelling case that Bayesian epistemology is not as false as many a critical rationalist might think, but that it could more properly be thought of as an important part of critical rationalist epistemology, which ultimately explains Bayesian reasoning. I enjoyed Bruce's unique and compelling take here, and I hope someone else gets something out of this.

[00:01:37]  Bruce: Welcome to The Theory of Anything podcast.

[00:01:39]  Unidentified speaker: Hey, Peter.

[00:01:40]  Unidentified speaker: Hello, Bruce.

[00:01:41]  Unidentified speaker: How are you doing today?

[00:01:43]  Unidentified speaker: Good.

[00:01:45]  Unidentified speaker: All right.

[00:01:46]  Bruce: You know, we've been wanting to do an episode on Pascal's Wager for like forever.

[00:01:52]  Unidentified speaker: So we're going to finally do it.

[00:01:53]  Bruce: We're going to do Pascal's Wager.

[00:01:55]  Unidentified speaker: Okay.

[00:01:56]  Bruce: Which is the beginning of probability theory, or one of the beginnings of probability theory. There's an excellent little book that I suddenly can't remember the name.

[00:02:07]  Unidentified speaker: It's in my notes here though.

[00:02:08]  Bruce: I'll give you the name here in a second when I get to it in my notes. That's by Ian Hacking, which is a history of probability theory. And I'm actually pulling a lot of this from that book. And I want to do like a separate episode on his book, which is a excellent but difficult book. And I never quite was sure if I got his point or not. So I kind of want to do an episode on just that and show how probability theory developed, what ideas came together to develop probability theory. And I think it's pretty interesting. In and of itself, it tells you something about probability theory. One of the main things that developed probability theory, according to Ian Hacking, who is someone who's studied this better than anybody, is Pascal's Wager, that it actually played a huge role in the development of modern probability theory.

[00:02:59]  Peter: Okay, well, I've been curious about what direction you're going to take this about Pascal's Wager. And that's not something I had even thought of.

[00:03:09]  Unidentified speaker: That's really interesting.

[00:03:11]  Unidentified speaker: I had no idea.

[00:03:12]  Unidentified speaker: Yes.

[00:03:13]  Bruce: Okay, so Pascal's Wager dates to around 1658. It's the first real idea of what we now call decision theory. Now on the surface, it's a religious argument, a case for believing in God. But its real importance is mathematical. Pascal showed that the logic of games of chance could be applied to almost any decision made under uncertainty. He took probability beyond simple dice problems, that previously that is all it had been used for, and turned it into a tool for deciding what to do when you can't know the outcome. In effect, he treated life as a game with stakes. He saw that as analogous, and he believed that you could apply probability theory to such an outcome, even though it wasn't in and of itself based on frequencies. Along the way, he introduced ideas that we still use today, dominance and mathematical expectation. He invented those with Pascal's wager. He weighed the payoff of salvation against the odds that God exists. In doing so, the wager captured the dual nature of probability that is still being debated today. It's not just about how often things happen in the world, i.e. frequencies, it's about how much we believe them, or so argues Ian Hacking. In his excellent history of probability theory, the emergence of probability, a philosophical study of early ideas about probability, induction and statistical inference.

[00:04:48]  Peter: Well, I'm just looking this up a bit on ChatGPT, and so far what you're saying checks out. It's the he was a he was into he this was a blaze, Blaise Pascal 1623 to 1662. But he was a French mathematician, physicist, inventor and religious philosopher. And it sounds like what you're going to say is he's the first Bayesian or something or one of the first.

[00:05:18]  Bruce: Well, you probably I don't know if I don't know if you would consider him the first Bayesian, but what he came up with was fundamental to what Bayesians now do. Like he invented the first part of Bayesian reasoning. So obviously, Bayes, Thomas Bayes is another famous religious philosopher.

[00:05:38]  Unidentified speaker: And he came after, didn't he?

[00:05:40]  Unidentified speaker: Yeah, he did.

[00:05:41]  Unidentified speaker: Okay.

[00:05:42]  Bruce: So at least I think he did.

[00:05:43]  Unidentified speaker: Check that with ChatGPT.

[00:05:44]  Unidentified speaker: I'm pretty sure he did.

[00:05:45]  Unidentified speaker: A little bit at least.

[00:05:47]  Unidentified speaker: Yeah.

[00:05:48]  Bruce: So but even Bayes wasn't the true inventor of Bayesian reasoning either. Like each of them kind of built on top of each other and brought something new to the table. And I think you could argue that Bayesian reasoning started with Pascal in a primitive form, and then didn't really mature into what it is today until, until honestly probably Jaynes, right? Who we're going to be quoting today. So certainly if you're a Bayesian epistemologist, you at least believe you owe a lot to Pascal, Bayes, Jaynes, etc.

[00:06:24]  Unidentified speaker: Right?

[00:06:25]  Unidentified speaker: Yeah.

[00:06:26]  Bruce: So Pascal's wager was pivotal to modern probability theory and decision theory. It helped generalize probability into the statistical powerhouse we rely on today, especially in machine learning. And yet it's one of the most hated and most maligned examples in the whole history of ideas. So Ivan Phillips, Ivan the Bayesian, I call him, who we've had on the show, went to a rationalist meetup. And he's obviously an atheist rationalist type, so he would fit in well at such a meetup. But he found that most of the rationalists there hated Bayesianism.

[00:07:05]  Unidentified speaker: Oh, is that right?

[00:07:06]  Unidentified speaker: Yeah, they saw it as supporting Christianity, thanks to Pascal's wager, and they were against Christianity, so they did not like Bayesianism.

[00:07:15]  Unidentified speaker: Really?

[00:07:16]  Unidentified speaker: Okay.

[00:07:16]  Unidentified speaker: Yes.

[00:07:17]  Bruce: So Richard Dawkins and other militant atheists have spilled a lot of ink trying to show what's wrong with Pascal's argument. But if hacking's careful history is correct, there's just no denying its central place in the history of ideas.

[00:07:33]  Unidentified speaker: Okay.

[00:07:34]  Bruce: So there are three parts to Pascal's argument. The argument from dominance, the argument from expectation, and the argument from dominating expectations. So let me walk you through the three levels of explanation or argument that he made as he received criticism and then continued to improve his argument. So Pascal's first version of the wager was what modern logicians call the argument from dominance. It's the simplest form of a decision problem. In decision theory, a strategy dominates when it does better in at least one scenario and no worse in every other scenario. So it's never the wrong call.

[00:08:12]  Unidentified speaker: It's always the right call, in other words.

[00:08:14]  Bruce: Pascal sets up just two states of the world. Either the Christian God exists or he doesn't. Starts with the case, so start with the case where God doesn't exist. Here Pascal assumes a religious life and worldly life out come out about the same, a finite life and then nothing. But if God doesn't exist, the two does exist rather, the two paths split sharply. Bet against God and you face eternal damnation. Bet on God and you gain eternal salvation. Salvation is infinitely better than damnation. And if God isn't there, the pious life costs you nothing under this version of the argument. So believing is the dominating choice. It wins in one world and it ties in the other world. Pascal knew you couldn't simply decide to have faith, but this is an important part of his theory that often gets overlooked. He believed you could choose to live as if you believed. And you could do the rituals, the holy water, the sacraments, et cetera. And that genuine belief would eventually follow, or likely follow, maybe. Now, there's a fair objection here. Maybe for some people, giving up worldly pleasures for pious life is staking too much. So this pushed Pascal to sharpen his case into what's called the argument from expectation. The first argument assumed a pious life cost nothing. This version admits that if God doesn't exist, a worldly life, even a life of sin, might for some people actually be more enjoyable than a cloistered one. To settle that, Pascal brings in the policy of maximizing expectations. You judge a decision by weighing the value of each payoff against the odds of it happening.

[00:09:58]  Bruce: So you take the value of the payoff, you multiply it by the odds of it happening.

[00:10:02]  Unidentified speaker: That's the expectation value.

[00:10:04]  Bruce: So he asks you to assume an even chance in this version of the argument, a probability of one half, that God exists.

[00:10:12]  Unidentified speaker: Why would he do that?

[00:10:14]  Bruce: We need to probably talk about that, because of course, this is probably in most people's minds, the problem in his argument at this point. So the reason why is because if you don't have any reason, even in modern probability theory, even in modern Bayesian reasoning, if you have no reason to prefer one theory over another, typically you treat them as equal probable. So you simply take all the options and you split the probabilities evenly. That is so commonly done in practice. So basically, he's just assuming equal probability, and that's not necessarily an insane thing for him to do, to assign half chance that God does exist and half chance that God doesn't exist. So he argues that even at those 50-50 odds, an incomparably greater value of eternal salvation outweighs any finite worldly joys. So salvation is infinite, worldly pleasures are finite. So the expectation value of the religious path, far x exceeds the secular one. So his conclusion, a rational person should take the pious path because it carries the highest expected value. Hacking notes that the logic is valid, but it rests on what he calls a, quote, monstrous premise that we just assign a 50-50 chance to the existence of God. For his final version of his argument, which is going to be called the argument from dominating expectation, Pascal takes on the skeptic, the person who thinks that God's existence is wildly improbable.

[00:11:47]  Unidentified speaker: His key move is this.

[00:11:49]  Bruce: As long as there's some finite chance God exists, however tiny, the whole machinery of the wager still holds. Because the reward of salvation is infinite, and multiplying infinity by even a minuscule probability, and you still get infinity. Worldly pleasures, by contrast, are always finite. So the infinite expectation of the pious path beats the finite gains of a secular one. No matter how small the odds. That makes this third version the strongest. It doesn't ask you to accept any particular probability, like 50-50, it only asks that the probability isn't exactly zero. As before, Pascal's aim is practical. Get the skeptic to live piously, the rituals and the sacraments, etc. And trust that real belief will follow.

[00:12:40]  Unidentified speaker: Hacking's point is this.

[00:12:44]  Bruce: This showed how the structure of games, of chance, could model decisions in any part of life where we act on inconclusive evidence.

[00:12:57]  Unidentified speaker: And here's the deeper point.

[00:12:58]  Bruce: Pascal's wager was pivotal in creating the idea that probability isn't about frequencies, how often things happen, in other words, but also about our credences, our degrees of belief in a theory. To put it more in more critical rationalist terms, even if you find belief in God implausible, you can't claim to know for certain there's no God due to fallibilism. And as long as that's true, or so goes this argument paired with this infinite reward, a belief in God would always rationally dominate, or so argues Pascal.

[00:13:38]  Unidentified speaker: So how good is Pascal's argument?

[00:13:40]  Unidentified speaker: Let me—actually, Peter, before I go on to make my own argument about how good or bad Pascal's argument is, what's your...

[00:13:50]  Bruce: How do you feel about it so far based on me just laying out Pascal's argument as best I can in a steel man form?

[00:13:57]  Peter: Well, I mean, my initial inclination is it sounds pretty, and I guess I still... It still seems a little old-fashioned or something strange. Like, maybe I can imagine someone taking it seriously 300 years ago, but...

[00:14:22]  Unidentified speaker: It's hard for you to take seriously.

[00:14:24]  Unidentified speaker: It's hard to...

[00:14:25]  Peter: Yeah, that's a good way to summarize it. Hard to take seriously, but that's really interesting what you're saying about the... I mean, there's a certain logic there that, like, there's in...

[00:14:35]  Unidentified speaker: So the gain...

[00:14:36]  Peter: The gains for believing in God are potentially infinite. So even if there's a tiny percent chance that the claims of Christianity or religion are true, then we should just accept them. But, I mean, it's kind of one of those things where there's some logic there, but it's like, it feels a little...

[00:15:05]  Unidentified speaker: I'm not going to stake my life on that, I guess.

[00:15:07]  Unidentified speaker: But...

[00:15:09]  Unidentified speaker: OK.

[00:15:10]  Bruce: You know, I think almost everybody feels that way.

[00:15:13]  Unidentified speaker: About...

[00:15:14]  Bruce: One of the things I'm going to argue here is that the only... That people only take Pascal's Wager seriously when it happens to support the view they already hold.

[00:15:24]  Unidentified speaker: Fair enough.

[00:15:25]  Bruce: And they never take it seriously when it goes against their view.

[00:15:29]  Unidentified speaker: Yeah.

[00:15:31]  Unidentified speaker: There's...

[00:15:31]  Unidentified speaker: So why?

[00:15:32]  Bruce: Like, why is that true?

[00:15:33]  Unidentified speaker: OK.

[00:15:33]  Bruce: That's really the question I want to try to answer today.

[00:15:36]  Unidentified speaker: OK.

[00:15:37]  Unidentified speaker: So how good is Pascal's argument?

[00:15:39]  Bruce: So it won't surprise longtime listeners that I think the argument is wrong, at least in the form Pascal put it. But what has surprised me is how hard it seems to be for atheists to pin down what's actually wrong with the argument. They get their counterarguments wrong again and again, in my opinion. Even the Bayesians, even the ones who've built their whole rational worldview on probability theory, it seems to me absolutely get their arguments against this Pascal argument wrong. So let's take a few of the arguments from Richard Dawkins, who has used against it. So first, he argues, quote, Believing is not something you can decide to do as a matter of policy. At least it is not something I can decide to do as an act of will. I can decide to go to church and I can decide to recite the Nicene Creed, and I can decide to swear on a stack of Bibles that I believe every word inside them. But none of that can make me actually believe it if I don't. Pascal's wager would only ever be an argument for feigning belief in God.

[00:16:50]  Unidentified speaker: So this actually fits well with Ray Percival's argument that we've discussed in recent podcasts, that you don't actually control your beliefs, that you have a rational mechanism that determines your beliefs, and you don't have control over, you don't as an act of free will decide what your beliefs are.

[00:17:08]  Unidentified speaker: And I've said that's true.

[00:17:10]  Bruce: I've had that absolutely happen to me where against my will, my beliefs have changed numerous times actually. So, of the arguments I've seen Dawkins and other atheists use, this is his only one that has at least some merit, in my opinion, because at least it points to a real problem. So Pascal assumes that choosing to act as if you believe will eventually produce genuine belief. And that really is a questionable assumption. And if it's false, that does seem to pose a problem for his argument. But it's maybe not as crazy wrong an assumption as Dawkins is indicating. There's a truth about human nature here that Pascal is capturing, one that honestly modern experiments have actually confirmed in the laboratory, okay? Think about our episode on dogmatism, not a mistake, we did the dogmatism episode first on self-deception and dogmatism. On the other hand, we do accept Ray's argument that you can't just choose your beliefs, which lines up with Dawkins' view. On the one hand, I mean, on the other hand, humans genuinely do deceive themselves, clinging dogmatically to an idea when it's a huge part of their identity.

[00:18:23]  Unidentified speaker: Both of these are true at once.

[00:18:25]  Unidentified speaker: They just are, okay?

[00:18:27]  Bruce: And there's no contradiction in them at all.

[00:18:30]  Unidentified speaker: They can both be true at once.

[00:18:32]  Bruce: Now imagine if Dawkins actually took Pascal's wager seriously, like pretend like he really took it seriously, which I'm going to argue he doesn't, okay? And he thought it through, and then he decided, oh, Pascal is right. I better start going to church and hoping I come to believe. There's an assumption buried in Dawkins' argument that is at least as questionable as Pascal's, and that is that if Dawkins made this a real part of his life, that he can somehow know now for sure that that would not cause him to have a change of heart. Let me suggest that Dawkins does not know that. He can't predict something like that about himself precisely because we don't control our beliefs.

[00:19:19]  Unidentified speaker: Just like Ray argues, that happens to cut both ways.

[00:19:23]  Peter: But it does seem to me that, you know, as I'm reflecting on this, that probably many people do, maybe not formally, but at least in their heart, I can imagine who go to church and maybe have doubts, maybe a lot of doubts, maybe some of them don't believe.

[00:19:47]  Unidentified speaker: But on a certain level, they're probably thinking, well, maybe if I go to church and go through the motions and all this, it does, I mean, religion does make people happier.

[00:20:01]  Unidentified speaker: There's—there's empirical evidence for that.

[00:20:03]  Unidentified speaker: There's empirical evidence of that, yes.

[00:20:05]  Unidentified speaker: For sure.

[00:20:06]  Unidentified speaker: And there's also just, you know, of course, it makes people happier.

[00:20:11]  Unidentified speaker: To—to be part of a community and to believe the same thing and to raise your children as part of this—this—this institution.

[00:20:21]  Unidentified speaker: I mean, obviously there are downsides to that too, but I think I—I—I maybe, you know, actually maybe it does make some sense in a way to just try to believe, if you can.

[00:20:35]  Unidentified speaker: So, okay.

[00:20:36]  Bruce: So that's exactly what I'm getting at, right?

[00:20:38]  Unidentified speaker: Yeah.

[00:20:39]  Bruce: So picture Richard Dawkins actually doing this.

[00:20:42]  Unidentified speaker: Okay.

[00:20:42]  Bruce: So let's be clear what we're talking about, okay?

[00:20:45]  Unidentified speaker: Yeah.

[00:20:46]  Bruce: Picture Richard Dawkins giving up his atheist friends, going to church, taking part in the rituals, even though he doesn't yet believe in them, making new friends in church, joining a religious community, coming to love the people that he is now friends with in this religious community. Might he at some point at least start to doubt his doubts, just enough to get something out of it? So I'm not saying that I know for sure he would. Pascal may be thought for sure he would, and I'm not going that far. I'm saying that Dawkins doesn't actually know either what's going to happen.

[00:21:25]  Unidentified speaker: He's human.

[00:21:26]  Bruce: He might come to accept, at least that maybe there's something to all this. Now, we've covered in episode 56, Rationality, Religion, and the Omega Point, we've covered a real life example of this, okay? What I just described, only using Richard Dawkins, is what really happened to Tolstoy in real life. Tolstoy gave up his elite atheist friends because his life was terrible and he could not find meaning in his life. He joined a church, he hung out and stayed, even though he's part of the rich elite, he hung out with the common people at church, started befriending the common people there, and for him, it actually changed his beliefs. Tolstoy's beliefs changed just like Pascal thought it would, okay, even though he went into it not believing. Suppose you did accept Pascal's argument, even if you didn't believe right now, it would at least be worth a try due to the high payout value. Since you can't be sure you won't come to believe, why not at least try to believe?

[00:22:31]  Unidentified speaker: Or to put this another way, there is at least a slim chance Dawkins would change his beliefs due to his choice of actions, which, you guessed it, now means Pascal's wager again dominates.

[00:22:44]  Bruce: So let me suggest that Dawkins isn't really rejecting Pascal's wager because of this argument, that he must actually be rejecting it on other grounds. If this were really rationally the reason why he was rejecting Pascal's wager, he would actually have to accept Pascal's wager because now you just have a chance you will believe with a small chance that God exists and that's still infinite payout. Nothing would change, it would still dominate. So what might be Richard Dawkins' actual grounds for disagreeing with Pascal's wager if it's not this?

[00:23:23]  Bruce: How does this fit into probability theory, if at all? So the last objection at least pointed to a real problem, even if it can never actually be used to dismiss Pascal's wager. So this next one, even though it's such a common atheist argument, is in my opinion, not even that good.

[00:23:43]  Unidentified speaker: It's a much worse argument in my opinion.

[00:23:45]  Bruce: The argument I have in mind is the idea that Pascal is wrongly assuming it's either the Christian god or no god at all. Okay, so you might say, but what if the Muslim god is the real god? So Dawkins argues, quote, the cost of failure is very high. But what if you choose the wrong god to believe in? What if you get up there and it's not Jehovah but Baal? Again, let's admit this is a legitimate problem at least with Pascal's original formulation. If it turned out to be the Muslims had the one true god and the Christians didn't, that would be bad for the Christians. Though it would be good for the Muslims, obviously. Either way, it's bad for atheists. And this is the problem with Dawkins actually making this argument. The objection misunderstands something important about probability theory, something I want to call out and make explicit. Or Bayesian version of probability theory, I should say, not necessarily the real probability theory. So I've had some real life discussions about Pascal's wager with Ivan, who's a Bayesian.

[00:24:49]  Unidentified speaker: And he's an atheist.

[00:24:50]  Bruce: So he dismisses Pascal, he [once/wants?] to me, dismiss Pascal's wager like this. Who knows, maybe the one true God will choose to reward atheists in heaven and burn all believers in him in hell. And with that, Ivan believed that he had offered an equally plausible alternative, assigned it an equal probability, and he considered his argument complete because he now had spread the probabilities to be equal. So I argued back to Ivan that his reasoning is, in my opinion, deeply and even profoundly flawed. As a critical rationalist, I consider this argument entirely ad hoc. So I would dismiss it on those grounds. But let's say I did accept Bayesian epistemology, which I don't, but let's say I did. It still seems to me that this argument just does not work even under Bayesian epistemology. To understand why, let's start by assuming the probability that God exists is very, very, very small. Say it's one in a billion, or if you prefer one in a trillion, or if you prefer one in a billion to the trillion. So I don't care what probability you assign it, as long as it's not zero, as long as it's a little tiny probability. What we're really arguing over now isn't the odds that God exists, but what God's nature would be, assuming He does exist. So the odds of His existence play no role at all now. No matter how tiny you made them, they're now irrelevant to the conversation. What we're discussing now is how plausible is each competing concept of God.

[00:26:22]  Bruce: Once you realize that's the question that you're now debating, Dawkins' argument for Baal being the one true God becomes deeply problematic. Baal's followers got wiped out.

[00:26:32]  Unidentified speaker: Doesn't that prove he doesn't exist?

[00:26:35]  Bruce: Well, maybe not, says the naïve Bayesian militant atheist. Maybe Baal just doesn't care about having followers. So the fact they all got wiped out tells you nothing about his existence. Okay, fair enough. That's an ad hoc argument. I again dismiss it as a critical rationalist on those grounds. But right now I'm playing the Bayesian, so let's accept it, okay, for the sake of argument. But that's now part of your explanatory structure, that Baal doesn't care about having followers. So why is he rewarding them for following him? Okay, no worries, says the naïve, militant, atheist Bayesian.

[00:27:12]  Unidentified speaker: Baal is just weird that way.

[00:27:13]  Bruce: He doesn't care about followers, but he rewards them anyway and damns everyone else to hell. Okay, that's now your theory.

[00:27:23]  Unidentified speaker: Let's stick with it.

[00:27:24]  Unidentified speaker: How plausible is that explanation compared to the Christian one?

[00:27:28]  Bruce: So in the Christian one, God made the world for a reason.

[00:27:31]  Unidentified speaker: He has a plan.

[00:27:32]  Bruce: He intends the best for his followers or for some Christian religions. He intends the best for absolutely everyone. He wants to impart important truths to help us along. He only wants people to believe in him because he knows that's what's best for them. It's not that he desires worship or something like that. If these are your competing theories compared to the ball one we just went over, I've got bad news for Richard Dawkins. One of these theories is a lot more plausible than the other. We could also extend this to the Muslim argument, like so. Sure, we don't know if you should be a Muslim or a Christian, but at least you have a 50-50 chance of avoiding burning in hell, so at least don't be an atheist. So the Muslim argument isn't going to buy the atheist anything. We could also point out how implausible it would be for a small cult to happen to be the one true religion, compared to, say, the great religions of the world that have a long history. This reduces our guessing in terms of plausibility arguments to just the so-called big five religions, giving you a 20 percent chance if you randomly select joining one religion, while the poor atheist has a 0 percent chance, or whatever the tiny probability we would want to assign to the utterly implausible explanations that we're dealing with to try to get the atheist into heaven. So this argument Dawkins is trying to invoke just does not save him from a Bayesian standpoint at all.

[00:29:03]  Bruce: This is also what's wrong with Ivan's argument, in my opinion, that maybe God wants to damn everyone who believes in him and reward everyone who doesn't. There's a subtle Bayesian error being made here, although a common one. The issue is that Bayesian probability does not tell you how to assign priors. Bayesians do understand this problem, but rather than admit defeat, they tend to make crap up. This is exactly the main problem with Bayesian epistemology. They check their gut, they decide what the prior should be, and by checking their gut subjectively, and they go with that as if it's meaningful. The result is exactly what you expect. They tend to weaponize their priors. The atheist Bayesian is happy to point out that God existing is implausible. They don't want to give it an equal probability of 50-50. And on those grounds, they will assign it, based on their gut, a very low prior probability, based purely on how implausible it sounds to them. But the moment they want to want their own explanation to win, they suddenly start treating all theories, no matter how implausible sounding, as equally probable. This is what we're really seeing happen here. They're assigning equal probability to the Christian God and to a trickster God who rewards atheists and damns believers for no reason at all. This is, if I may be bold, rather convenient an argument and surely incorrect reasoning, even under Bayesian epistemology. It weaponizes Bayesian reasoning by doing this.

[00:30:41]  Bruce: Assume equal probability when that comes out in your favor, but judge by the plausibility soundness of the explanation when it comes out in your favor. Using these two rules, you can obtain, you can decide anything you want as the outcome. It is meaningless in terms of rationality now. Note that by comparison, Pascal's original argument never falls into this mistake because it is an argument by dominance. In short, if this is your reasoning for rejecting Pascal's wager, you are, in my opinion, reasoning incorrectly. Does this all mean that I'm therefore arguing for Pascal's wager? Perish the thought. I think Pascal's wager is fundamentally flawed. In a way, these other arguments have completely failed to capture.

[00:31:34]  Unidentified speaker: Let me show you my own approach to it.

[00:31:36]  Bruce: Okay, so now, first of all, I am a Latter-day Saint, formerly called Mormons. I've often faced Pascal's wager from evangelical Christians. So, let me explain the evangelical versus LDS variant of Pascal's wager. It goes something like this. I've had people numerous times raise this to me, by the way. Latter-day Saints believe nearly everyone goes to heaven, though they believe in multiple heavens with tiered rewards. So in LDS theology, an evangelical goes to heaven. But in evangelical theology, a Mormon will burn in hell forever. Thus, by Pascal's wager, you should choose to be an evangelical, not a Latter-day Saint. The most common place I've heard this version of Pascal's wager was on my LDS mission, from obviously antagonistic evangelical Christians. But I've seen highly educated, thoughtful evangelical Christians use this argument. In the book How Wide the Divide, the well-known evangelical scholar, Craig Blomberg, makes almost exactly this argument, though in the context of the evangelical versus LDS view on the grace of Christ. Now, I deeply respect Blomberg, and unlike a lot of evangelical Christian scholars, I find him to be genuinely, genuinely respectful of Latter-day Saints. Yet Blomberg sincerely thought this was a good argument.

[00:33:07]  Unidentified speaker: It's not.

[00:33:08]  Bruce: Let's talk about why it's such a bad argument. There are two problems with this argument. One is the weaker and more obvious. So I would say ultimately wrong because it relies on Bayesian epistemology. The other is stronger and less obvious, but ultimately right. Let's take the weaker wrong argument first. If you accept Bayesian epistemology, and I don't, then it suffers from the very same problem as the Dawkins-Bayesian argument from earlier. Even if I accepted this as a real decision theory problem, and as we'll see, I don't. The argument still doesn't work. If anything, it's a strong argument for evangelicals converting to Mormonism, not the other way around.

[00:33:47]  Unidentified speaker: Here's the setup.

[00:33:49]  Bruce: We start by assuming there is a god, and he is the Christian god, since obviously this is a debate between evangelical Christians and Latter-day Saints. Both are Christian, both accept the Christian god. So it makes sense to use that as our starting assumption. So we're really arguing over which version of Christianity is more plausible, which interpretation of Christianity is more plausible, maybe. So two hypotheses are on the table. One, a god who damns people to burn in hell forever, even sincere believers like Latter-day Saints, for getting their beliefs about him slightly wrong. Or two, a god who damns few or none to hell forever, but gives an infinite reward to those who believed more correctly. Note that that might be even after your death in LDS beliefs. You do not have to actually get the correct beliefs in this earth life in LDS beliefs. Perhaps you will argue both of these are implausible. If you're an atheist, you're going to argue both of these are implausible. But that doesn't matter at the moment. The question on the table that we need to answer is only which of these two is the more plausible version of Christianity.

[00:34:55]  Unidentified speaker: Now, let me state the obvious.

[00:34:57]  Bruce: A, quote, perfectly loving god who damns people to burn forever in hell is, rationally speaking, pretty embarrassing. It's no accident that even many Christians today are dropping that doctrine, even though it has a long history, because it really is a flat contradiction.

[00:35:13]  Unidentified speaker: But here's the thing.

[00:35:14]  Bruce: Even granting how implausible the evangelical god is, couldn't you still argue that burning forever is so bad that you should hedge, you should accept a lesser heaven just in case? Now, given the bad assumptions Pascal Wager is built on, I could at least see, if you were accepting them, I could at least see that as a plausible move.

[00:35:35]  Unidentified speaker: But a Latter-day Saint has an easy counter.

[00:35:37]  Bruce: The highest heaven is infinitely better than the next one down. So in LDS theology, the highest heaven means becoming one with God, in a sense, becoming God yourself. And becoming fully like God is an infinite reward. How could it not be? So, here goes the argument, it offsets an infinite punishment. So I don't see how evangelicals come out ahead. If we're accepting Pascal's Bayesian style reasoning, then it seems like they've lost. They've only made their theory less plausible to try to make this argument. And unless they want to claim an infinite punishment isn't offset by an infinite reward, a move that I doubt they'd even consider, they haven't moved the reward values. They're both, there's one's infinite negative, one's infinite positive, and theirs is the less plausible explanation, probably by a large margin, if we're only considering these two. So if this Bayesian argument were a correct argument, and again, I insist it is not, evangelicals would lose this battle on rational grounds. One thing that we need to notice here, nobody who invokes Pascal's wager actually seems convinced by it. An evangelical Christian is happy to invoke it against an atheist who remains completely unfazed by the argument. But that same evangelical would never dream of converting to Mormonism, even though their own logic makes it so that they should. So let's admit it, there's something deeply unconvincing about Pascal's wager, in practice at least. We sense something is wrong with it, even that we feel free to ignore what it says.

[00:37:23]  Bruce: We're only unsure what that something is that is wrong with it, and we try to explain it, and most of our explanations just don't make sense. What I'm driving at is a deeper problem, harder to pinpoint, with the very idea of Bayesian reasoning and how it gets used, or I'd say weaponized by so-called Bayesian epistemologists today, to really see it, you need to look at an argument that's very similar to Pascal's wager that was invented by Eliezer Yudkowsky, famously the Bayesian who's the anti-AGI guy. He has a thought experiment called Pascal's mugging. So here's Yudkowsky. He says, now suppose someone comes to me and says, give me $5 or I'll use my magic powers from outside the matrix to run a Turing machine that simulates and kills three to the three—three to the power, power, power, power, power, three people. So very, very, very large number. If Pascal's wager is correct, the reasoning of Pascal wager is correct, then you should hand this guy $5. Because even though it's really improbable that this guy actually has those powers, the level of damage he's the payout value for that low probability dominates the $5. So you should just hand over the $5 if you believe Bayesian reasoning is correct. Okay, so Yudkowsky tries to use Solomonoff's universal prior to escape this. So quote, the Solomonoff inductive probability, two to the negative Kolmogorov complexity is exponentially tinier than one might naively think. But small as the probability is, it isn't anywhere near as small as three to the power, power, power, power, power three is large.

[00:39:12]  Bruce: If you don't know what Solomonoff's universal prior is, don't worry about that for now. It's a way to assign priors to theories based on how computationally complex they are. It's a fascinating idea worthy of discussion, and I want to eventually build up to doing a podcast on that. I have to kind of explain a lot to get to the point where it would make sense.

[00:39:32]  Unidentified speaker: Here's the thing, though.

[00:39:33]  Unidentified speaker: It's incomputable.

[00:39:34]  Bruce: So it never really can help you in real life.

[00:39:37]  Unidentified speaker: Okay.

[00:39:38]  Bruce: Of course, you could just ignore the universal prior here. It's not as if it's actually calculable because it's incomputable. You might simply do what Bayesians usually do here. That is, make crap up and just arbitrarily assign a prior even tinier than three power, power, power, power, power, three.

[00:39:59]  Unidentified speaker: But this won't do.

[00:40:01]  Bruce: Because the mugger can simply keep raising the threatened punishment until it once again overwhelms whatever tiny probability you assign. He can add additional power, let's say. So there is literally no way to overcome Pascal's mugging within the Bayesian epistemological framework. Yudkowsky all but admits this, quote, I don't feel, it doesn't feel to me like three power, power, power, power, power, three lives are really at stake, even at very tiny probability. I'd sooner question my grasp of, quote, rationality than give five dollars to Pascal's mugger because I thought it was, quote, rational. Continuing, he says, if I could formalize whichever internal criterion was telling me I didn't want this to happen, I would have an answer. So Yudkowsky himself, he just cannot see a way to solve this within the Bayesian epistemological framework. Quote, I've talked over a variant of this problem with Nick Hay, Peter de Blanc, and Marcello Herreshoff in summer of 2006. I don't feel I have a satisfactory resolution as yet. So I'm throwing it open to any analytic philosophers. He's still, to this day, trying to find an answer to this problem. By the way, good on Yudkowsky to actually publish a known problem with his epistemology. That's absolutely the right thing to do. Yudkowsky goes over attempts to solve Pascal's mugging by ad hoc assigning a leverage ratio to tweak the probabilities. So basically you say, oh, in this scenario, I'm going to assign an even lower probability because the probability that this guy would happen to select me, that itself is low.

[00:41:47]  Bruce: It's just basically an ad hoc way of trying to reduce the probabilities until you get what you intuitively feel the right answer is. It's an example of making crap up.

[00:41:56]  Unidentified speaker: Okay.

[00:41:57]  Unidentified speaker: So here's the problem.

[00:41:59]  Bruce: Doing this works, but it creates a new problem. This is because assigning a very tiny prior probability to something has its own problems. So Yudkowsky calls this new problem Pascal's Muggle. Basically, if you make the prior too tiny, then no possible evidence can move you because no human can receive a stream of sensory evidence with a likelihood ratio anywhere near that extreme. So in fact, this is that's a very empiricist worded way of saying it.

[00:42:29]  Unidentified speaker: That is the way Yudkowsky says it.

[00:42:31]  Bruce: It's not wrong though, because you simply can't receive evidence at a fast clip. You have to actually receive it, process it, understand it. So he's not wrong here, even if you don't like the empiricist framing. So effectively, you're now setting the prior to zero for all intents and purposes, once again, sufficiently small. Now, I thought after Yudkowsky wrote these articles, talking about this problem with Bayesian epistemology that he does not know how to solve. William Quixote, not his real name, obviously, he's a commenter, makes the following comment to Yudkowsky about his post on Pascal's mugging and Pascal's muggle. I thought this was very perceptive. So I'm going to read the comment in full. I don't like to be a bearer of bad news here, but it ought to be stated. This whole leverage ratio idea is very obviously an intelligent kludge patch workaround, because you have two base level theories that either don't work together or don't work individually. You already know that something doesn't work. That's what the original post was about, and that's what this latest post tries to address. But this is a clunky, inelegant patch that's fine for a project or a website, but given belief in the rest of your writings on AI, this is high stakes. At those stakes as saying, we don't know it doesn't work, but we patch the bugs, we know it doesn't work, but we patch the bugs we found, is not acceptable. The combination of your best guess at picking the right decision theory and your best guess at epistemology produces absurd conclusions.

[00:44:17]  Bruce: Note that you already know this, this knowledge which you already have motivated this latest post. The next step is to identify which is wrong, the decision theory or the epistemology. After that, you need to find something that's not wrong to replace it.

[00:44:34]  Unidentified speaker: That sucks.

[00:44:36]  Bruce: It's probably extremely hard, and it probably sets you back to square one on multiple points. But you can't know that one of your foundations is wrong and just keep going. Once you know you are wrong, you need to act consistently with that. This is a correct answer to both Pascal's Wager and Pascal's Mugging, and it's the same answer for both. None of the answers we've covered so far is the right one. They simply don't work. The correct answer is, we've refuted Bayesian epistemology with these examples.

[00:45:13]  Unidentified speaker: That is the correct answer.

[00:45:17]  Unidentified speaker: Okay.

[00:45:19]  Bruce: So now, let me explain what's actually wrong, and then we can start to make sense of what the correct answer here is and how it does away with Bayesian epistemology, okay, and replaces it with something much better. To get at that, let me ask, what is Dawkins really doing when he rejects Pascal's Wager? It can't be either of the arguments he gave. I just explained why those arguments do not work. If those were his real arguments, and he was rational, he'd be a Christian now, or possibly a Muslim, I guess. But honestly, if you accept Bayesian epistemology, then Pascal is right. One option, belief in God dominates, and you're done. You should believe as best you can, no matter how small the probability.

[00:46:12]  Unidentified speaker: So let me state the obvious.

[00:46:13]  Bruce: What Dawkins is really doing, what Dawkins is really doing, is assigning a probability of zero to God's existence.

[00:46:22]  Unidentified speaker: That's right.

[00:46:23]  Bruce: Whether he realizes it or not, Dawkins is assigning a probability of zero to God's existence. That's why he's unconcerned with Pascal's wager. So why doesn't Dawkins just admit that he's setting his prior probability of God's existence to zero? Because admitting this embarrasses him due to, I'm going to argue, a misunderstanding of epistemology. Bayesians have an idea that when a Bayesian thinker assigns a probability of one or zero to a given statement, it means that no evidence will ever change your mind.

[00:46:55]  Unidentified speaker: It means you're closed minded.

[00:46:57]  Bruce: Think about it this way. If you assign a one, you're certain it's correct. So nothing can reduce the value below one. And if you assign a zero, you're certain the theory is wrong. So no evidence can cause you to accept it later. Or so goes the argument from Bayesian epistemologists. Thus, assigning a probability of zero or one is understood by Bayesian epistemologists to be irrational. Dawkins would consider it embarrassing to claim that there is no chance at all that God exists. He'd essentially be admitting he isn't open minded and isn't open to reconsidering his own views in light of new evidence. Or this is epistemologically what I think he is thinking. Dawkins is making what we might call the Bayesian epistemologist's mistake. To avoid the charge of not being open minded, he refuses to admit he's setting his probability to zero. This is the same mistake Yudkowsky is making with Pascal's mugging. Both follow the Bayesian rule that you're never allowed to set a probability to zero. Two interesting notes about this quote unquote Bayesian rule. First, it is absolutely not part of Bayesian reasoning at all. Bayesian reasoning has no problem at all assigning a probability to zero or one to something.

[00:48:22]  Unidentified speaker: This is an important difference.

[00:48:25]  Bruce: One of a few incredibly important differences between Bayesian reasoning and Bayesian epistemology, okay? Bayesian reasoning has no rule against assigning zero or one. Bayesian epistemology has a rule against assigning a zero or one. There are a handful of other differences, but this is probably the most important difference. The other thing to notice is that Richard Dawkins is not a Bayesian, and in fact rejects Bayesian reasoning when applied to philosophical questions like this.

[00:48:58]  Bruce: He views personal or subjective probability as an unscientific thing, famously asking, who cares about subjective judgments anyway? So why is Dawkins, who is not a Bayesian, adhering to this Bayesian rule?

[00:49:15]  Unidentified speaker: The answer is somewhat surprising.

[00:49:17]  Unidentified speaker: It's actually—it isn't actually a Bayesian rule per se.

[00:49:22]  Bruce: This is actually a mistake made by most people, even ones that have never in their lives heard of Bayesian epistemology. So in the past, I've had a term for default epistemology that people hold. I've called it folk epistemology. Folk epistemology is my name for the default epistemological reasoning that a person has if they know nothing at all about epistemology.

[00:49:44]  Peter: They've never heard the word.

[00:49:46]  Unidentified speaker: Yes.

[00:49:47]  Bruce: So the cause and effects are backwards here. Bayesians are actually attempting to formalize a mistake in folk epistemology. An evangelical Christian who believes in Pascal's wager might agree with me that Dawkins is tacitly setting his probability to zero. And then that evangelical Christian is going to declare him close-minded. But because the evangelical Christian is also setting the probability to zero that Mormons might be more correct than him, pot, meet, kettle.

[00:50:20]  Unidentified speaker: Or maybe not.

[00:50:21]  Bruce: Let's consider another possibility that there is just nothing at all wrong with assigning a probability of zero to something. To see why, consider the more obvious case first. And then from there, we can start to unravel the less obvious cases. So Pascal's mugging is the more obvious case here. Notice what Yudkowsky is doing when he ignores the mugger. If Yudkowsky really accepted Bayesian epistemology, he would pay the mugger $5, but he doesn't. What Yudkowsky really does is this. He assigns a probability of zero to the mugger's claim, and he's done. And it turns out that's exactly the correct rational thing to do, given his understanding of the world. It's not even hard to see why. If a Pascal's mugger approached me, I would think to myself, there's a zero percent chance this person can do what he's claiming, because it contradicts my entire model of the world. Before I'd take his claim seriously, I'd need some reason to doubt my model first, falsify my model, if you will. A Popperian problem that would force me to conjecture a new model of reality, one with room for something like Pascal's mugger—mugger to exist.

[00:51:39]  Unidentified speaker: Now, that hasn't happened to me yet.

[00:51:41]  Bruce: So, I would, within my model, assign his claim a probability of zero.

[00:51:46]  Unidentified speaker: And that makes absolutely perfect sense.

[00:51:49]  Unidentified speaker: There's nothing wrong with this rationally.

[00:51:52]  Unidentified speaker: Given my understanding of the world, that's right, that's the correct answer.

[00:51:57]  Unidentified speaker: These are all the same thing.

[00:51:58]  Bruce: Dawkins doesn't accept God's existence as a realistic possibility. So, to him, Pascal's wager is meaningless, for the same reason none of us would pay Pascal's mugger. Likewise, an Evangelical Christian assigns a probability of zero to the Mormons being correct. So why is it so surprising that Dawkins assigns a probability of zero to the Evangelical Christian claim?

[00:52:19]  Unidentified speaker: Surely it doesn't indicate closed-mindedness.

[00:52:22]  Bruce: One can always revise the model later if a new problem requires it. But for the moment, their model doesn't allow for Pascal's mugger's claim, or for the Mormons being correct if you're the Evangelical Christian, or for God existing if you're Richard Dawkins, respectively.

[00:52:40]  Peter: So your claim is that Richard Dawkins, Yudkowsky, Evangelical Christians, Mormons, and anyone who subscribes to folk epistemology, they're all actually critical rationalists, but they don't know it.

[00:52:59]  Unidentified speaker: That's right.

[00:53:00]  Unidentified speaker: I actually agree with that.

[00:53:04]  Unidentified speaker: All right.

[00:53:04]  Bruce: So the key mistake is the Bayesian epistemologist mistake, the rule that you can never assign a probability of zero.

[00:53:14]  Unidentified speaker: That is the mistake.

[00:53:16]  Bruce: The rule is exactly what causes Bayesian epistemology to collapse into contradictions that Yudkowsky can't seem to resolve because they're contradictions. That's why he can't resolve them.

[00:53:26]  Unidentified speaker: They're not resolvable.

[00:53:28]  Bruce: They prove your epistemology false. And he will never until he abandons the Bayesian epistemologist mistake and returns to actual probability theory, which has no such rule. I've argued before on this podcast that probability logic is just a form of logic with the same limitations as deductive logic or any other kind of logic. The results you get from it are only as good as the assumptions you start with. If those assumptions are wrong, your conclusions are wrong too.

[00:54:01]  Unidentified speaker: It makes such perfect sense.

[00:54:02]  Bruce: It's hard to believe that people can't see this. Put simply, probability and so-called inductive logic is really just deductive logic, with an extension that allows you to present partial criticisms instead of simply refuted or not refuted. In reality, probability theory still has to deal with the Duhem–Quine problem and it still can be valid without being sound. And most importantly, nothing in probability theory can ever escape the problem of justificationism. We keep having to keep trying to give probability and so-called inductive logic magical properties it simply cannot have. Bayesians want evidence to imbue a theory with soundness instead of merely validity. This is what Bayesian epistemologists are trying to extract from probability theory, something that probability theory and true Bayesian reasoning simply do not offer. To see why probability can't escape the problem of justificationism, we need to draw a distinction between two kinds of probability. In Popper's epistemology, what you justify is not the theory itself, but your preference for the theory. So it's a relative to other theories that are on the table. At first, this might seem like a distinction without a difference.

[00:55:21]  Unidentified speaker: It's not.

[00:55:22]  Bruce: It's the heart of what Bayesians and folk epistemologists get wrong. Let's go back to the three balls example. So the example I've raised before is you've got a bowl, and you've got three balls in a bowl. You cover the three black balls in a bowl. You cover the bowl. If you have these three black balls in the covered bowl, there is no chance at all you'll draw a white one. Given the model, the probability is zero. That is the correct answer under Bayesian reasoning. That's even the way they teach it in school, okay? A Bayesian who says, but maybe you're in error, misses the point. All theories are conjectures, and any of them might be in error, but it's impossible to assign an absolute probability to your model being in error. As we'll see, that would require an infinite regress. This is the distinction between what we might call absolute probability versus model-dependent probability. Absolute probabilities are nonsensical.

[00:56:25]  Unidentified speaker: They do not exist.

[00:56:27]  Bruce: Model-dependent probabilities do exist, and they're real, and they're useful, and they're the true thing that Bayesian reasoning is dealing with. The probability of pulling a white ball from a bag or bowl of three black balls is zero. That's a model-dependent probability, the kind that exists, because it follows the probability calculus. But the absolute probability of pulling a white ball due to some undefined, untestable error, what's that? That's a nonsensical value. It does not follow the probability calculus, not in the given model, not in any. Can you see the difference between the two and why one is fine and the other one isn't? Put simply, you can measure a probability given a specific model, theory or explanation. What you cannot measure is the probability that the model, theory or explanation itself is correct. If you could, that would be a form of justificationism, a way to confirm a theory absolutely rather than just expressing a relative preference between theories. When we talk about well-behaved probabilities, the ones that follow the probability calculus, we always mean a probability given a set of starting assumptions, our background information, that is our conjectured theory or model. Bayesian reasoning is valid precisely because it's always model-dependent. Bayesian epistemology is false precisely because it tries to be independent of a model. The mistake folk and Bayesian epistemologists make is using probabilities to measure the probability that their model itself is correct. Or maybe you could put this a different way.

[00:58:12]  Bruce: If they're trying to measure the probability of a theory compared to every single possible theory, even ones that haven't been developed yet.

[00:58:20]  Unidentified speaker: Okay, that would be the same thing.

[00:58:22]  Bruce: Okay, where you're trying to measure the absolute probability of your theory. Notice this is exactly the mistake being smuggled into Pascal's mugging. Instead of saying, given my model of reality, the probability of the mugger's claim is zero, it sneakily switches to, what's the probability that my model of reasoning is wrong? But the moment it tries to answer that question, the contradiction of Bayesian epistemology surfaces immediately. This is precisely why Yudkowsky can't find an answer to Pascal's mugging. He fails to see the difference between measuring the probability of something within a conjecture model and measuring the probability that the model itself is correct.

[00:58:58]  Unidentified speaker: The first is fine.

[00:58:59]  Unidentified speaker: The second is justificationism in disguise.

[00:59:02]  Bruce: To put it bluntly, Yudkowsky's own Pascal mugger is an outright falsification of Bayesian epistemology. It shows that the framework is contradictory and that it needs to be abandoned for a better one. Yudkowsky can search as long and hard as he wants, but the answer will always be the same. Give up Bayesian epistemology and embrace Popperian epistemology. We've now drawn a clear distinction between Bayesian reasoning and Bayesian epistemology.

[00:59:26]  Unidentified speaker: I've asked this question so many times.

[00:59:27]  Bruce: What's the difference between it's like anytime you hear Deutsch talk or somebody in the CritRat circles talk about this, they'll say, oh, I'm fine with Bayesian reasoning. It's just Bayesian epistemology that I reject. But then you ask them, what's the difference between those two? And you get a really obfuscated answer. I think the best answer I've heard from Deutsch was, well, Bayesian reasoning deals with small worlds that are well-defined.

[00:59:52]  Unidentified speaker: That's not true.

[00:59:53]  Bruce: Bayesian reasoning absolutely does not have to deal with small worlds. That isn't the correct distinction between Bayesian reasoning and Bayesian epistemology. Bayesian reasoning is at its core model dependent, which makes, which that's what makes it real, valid, and useful. Critical rationalists ought to embrace Bayesian reasoning. It's a legitimate form of falsificationism. Bayesian epistemology is at its core model independent. That's why it's a false epistemology and why it leads to contradictions and poor reasoning. My claim is this, folk epistemology tries to measure the probability of the conjecture itself, and Bayesian epistemology tries to formalize that very mistake, borrowing the machinery of Bayesian reasoning to do so. That doesn't mean Bayesian reasoning is itself wrong. Okay, why do we humans with our built-in hard to shake folk epistemology, naturally try to measure the probability of the theory itself?

[01:00:49]  Unidentified speaker: Now, I think there are a few reasons for this.

[01:00:51]  Bruce: The first is that the language of probability predates the probability calculus. This isn't a small point, but you never really think about it. People spoke of things being probable before the probability of the calculus existed by centuries, okay, across multiple different languages, way back into history. Okay, so the word probability has a long history that's got nothing to do with the probability calculus. They only came to later be equated together. So today we try to equate the language of probability with the probability calculus. It's a natural enough mistake to make, okay? But in reality, the language of probability grew up model independent and so couldn't be formalized, and only later gave rise to the remarkable model dependent probability calculus. It never clicked for a lot of us that these are in fact two different things. There's really nothing wrong with saying, my theory is probably correct in some loose absolute sense, so long as you recognize that you're not using probability in the sense of the probability calculus. That's something that Popper used to always raise, that you can use the language of probability, but it doesn't necessarily match the probability calculus. But of course, we quickly get confused because both use the very same word. So soon we're [veering/very?] back into thinking of the probability calculus as being equivalent to the language of probability, and they're not the same thing. Second, there's a problem with what we might call the human ability to expand models on the fly. Let's take our three black balls example.

[01:02:33]  Bruce: Again, starting with a well-behaved Popperian style approach, suppose I show you three black balls in a bowl, and you can see them, so you know there are only three. Then I cover the bowl and I ask, what are the odds you'll pull a white ball out? Now, using model-dependent probability, you correctly predict zero, okay?

[01:02:56]  Unidentified speaker: That would make perfect sense.

[01:02:58]  Unidentified speaker: There's only three black balls.

[01:02:59]  Bruce: I'm asking you to tell me, given that there's only three black balls, what's the odds that you'll pull a white one? Obviously, the answer is zero. Then you try it and out comes a white ball. Now, what probably happens is you laugh, because you know that's impossible. So you assume, let's say correctly, that I palmed the black balls and swapped in white ones as part of a magic trick. Notice that you assess the situation correctly. You don't question your original probabilities. Zero was right, given the model you had at the time. Instead, you question the model itself. You think, okay, given this white ball, I clearly had the wrong model. I thought this was a simple probability exercise, but really it's a magic trick. This is the correct way to question a model and replace it with a new conjecture.

[01:03:52]  Unidentified speaker: That's the Popperian approach.

[01:03:54]  Bruce: Notice that your initial probability of zero did not mean you couldn't change your mind later. It did not indicate closed mindedness. What it really meant was that you couldn't change your mind later if you held your model constant, but you didn't have to do that. You can always question and even replace a theory or model. You hit a problem with your original conjecture and it forced you to conjecture a new one. So far, this is Popperian to the core and it's entirely rational. Now compare this to what a Bayesian epistemologist might try to do. They might want to measure up front the probability that their model is wrong.

[01:04:31]  Unidentified speaker: So they think something like this.

[01:04:33]  Bruce: Hmm, I can see there are only three black balls. So the probability of pulling a white one is zero.

[01:04:39]  Unidentified speaker: But I can't say that.

[01:04:41]  Bruce: I should never assign a probability of zero.

[01:04:43]  Unidentified speaker: That would mean I'm closed minded to evidence.

[01:04:46]  Bruce: And it would mean I could never change my mind later. So I better not say zero. Then they justify that decision by reasoning to themselves something like this.

[01:04:55]  Unidentified speaker: Maybe it's a magic trick.

[01:04:56]  Unidentified speaker: Maybe I'm hallucinating.

[01:04:58]  Bruce: Maybe aliens will swap the balls while I'm not looking. Maybe I'm wrong about physics and the nature of light.

[01:05:04]  Unidentified speaker: Maybe, maybe, maybe, maybe.

[01:05:06]  Bruce: Notice those are all ad hoc theories, by the way, at this point. And once you start considering every possible theory, including untestable ad hoc ones, there are infinitely many possible problems with the model. And the probability calculus breaks down when there are infinitely many options.

[01:05:24]  Unidentified speaker: You can't have that.

[01:05:25]  Unidentified speaker: So what does the Bayesian epistemologist do?

[01:05:28]  Unidentified speaker: Well, they make crap up, of course.

[01:05:31]  Bruce: They finally just say, I think there's a 99.99999% chance I'll pull a black ball, hedging their bets. And then they pull a white one, because it was in fact a magic trick all along. And dutifully run their Bayesian updates from there, rather than doing the sensible thing, treating their original model as falsified and conjecturing a new one. Note that because the Popperian and the Bayesian gets the wrong answer initially, both get the answer wrong initially, because the model was wrong. But once the Popperian sees the model was wrong, they quickly conjecture the right one, that the magician can pull any ball he wants out of his sleeve, whatever he needs to. The Bayesian, if we're being honest, I just said a moment ago, the Bayesian would then do his Bayesian updates. But if we're being honest, he won't actually do that. The Bayesian will actually be a critical rationalist here. No way is he really going to run a Bayesian update here, using the original .0001 figure as his prior for pulling a white ball. If he did, he would get the wrong answer. Consider the predicament the Bayesian epistemologist is now in. Suppose you pull the white ball out, which according to your model independent prior, had only a .0001 chance of coming out white. You return the white ball to the bowl and pull again. What does the Bayesian say your chance of pulling a white ball is?

[01:06:54]  Unidentified speaker: So if you're a Popperian, you already know the answer is 100 percent.

[01:06:57]  Bruce: If that's the magic trick, the magician switched all the balls.

[01:07:00]  Unidentified speaker: That's the correct answer.

[01:07:01]  Bruce: For the Bayesian, if you replace the ball, nothing updates. It's as if you had a bowl of 10,000 balls with just one white ball in it. You put the white ball back, and the odds don't change because you put the white ball back. You should really still predict 0.0001 percent chance of pulling a white ball again. But that's clearly the wrong answer. So let's assume no replacement instead.

[01:07:28]  Unidentified speaker: But you already pulled the white ball out.

[01:07:30]  Bruce: You're now left with only black balls remaining, supposedly, right? So the white still now equals 0, and 0 violates the Bayesian rule of never assigning a probability to 0. So the whole apparatus of arbitrary priors has failed to accomplish the one job it has, okay, to capture the chance that there's an error in the model. Either way, the Bayesian gets the wrong answer. The Popperian, meanwhile, has already moved on. The white ball falsified his model, and the magician switched the balls, and the answer is 100% chance I'm going to get a white one now. Of course, a sophisticated Bayesian, now that they know that this is a trick, would approach this differently after the fact. Now, here's the key that I want to argue here. Bayesians are actually Popperians, intuitively speaking, okay? When confronted with a situation like this, what they're going to do is they're going to retroactively change their model, conjecture a new model. They're going to conjecture one that makes sense with the data they've now seen. And then they're going to retroactively say, oh, see, this was Bayesianism all along. When what they really did was refute the original model and conjecture a new one.

[01:08:45]  Unidentified speaker: Okay.

[01:08:46]  Bruce: So they'd likely say, Bruce, you should really, what really should happen here is a Bayesian analysis. The chance that this is a trick versus the chance it's really a bowl with three black balls. There's actually an infinity of ways they could go about this. They could tweak the model in all sorts of ways. What I'm telling you would be a common way to do it, but it's still wrong and that's what I want to explain here. This is exactly what I mean though about the human ability to expand models on the fly. Now that you know a trick is possible, you could say after the fact, after you know it's actually a trick. Well, I'll fix this problem with Bayesian epistemology by simply rebuilding the model to include the probability of a trick.

[01:09:27]  Unidentified speaker: So they'd start with a competition of two theories.

[01:09:30]  Unidentified speaker: Now, they wouldn't have thought to have done this until after they already have refuted the previous theory.

[01:09:35]  Unidentified speaker: Okay.

[01:09:36]  Bruce: So we'd start with a competition of two theories. So hypothesis one, that this is not a magic trick, and hypothesis two, that this is a magic trick. Now the magic trick is part of the model, and the probabilities will behave properly, or so we're claiming, using Bayesian reasoning. But what you really did was expand the model after the fact. You've changed to a new model, you've conjectured a new model, adding that specific trick into the model.

[01:10:07]  Unidentified speaker: And once you've done that, sure, the Bayesian finds that they handle the situation just fine, sort of, because this new revised model now contains the assumption that it might be a trick.

[01:10:17]  Bruce: The whole thing quietly shifts from bad Bayesian epistemology back to good Bayesian reasoning, which gives the epistemologist the false impression that their epistemology could have handled the problem all along. When really, they're just on the fly changing the model to make it match what they know to be right through falsificationism. In fact, what saved them was a very, very human, very un-Bayesian leap, recognizing the model itself was wrong and needed to be replaced. The Bayesian then reasoned correctly within the new model, but the crucial step of knowing to build that model came from somewhere outside the Bayesian epistemologist framework entirely. Note also that this update to the model can't really save the Bayesian epistemologist, even if he had known upfront to include a magic trick as part of his model.

[01:11:07]  Unidentified speaker: Let me explain why.

[01:11:09]  Unidentified speaker: Here is how Bayesian would now do this update to the model.

[01:11:13]  Unidentified speaker: So H1 is the bowl is three black balls, and we're assigning a probability of 0.99999 to it.

[01:11:21]  Unidentified speaker: Hypothesis 2 is this is a magic trick.

[01:11:24]  Bruce: We're assigning a probability of 0.0001 to it. The evidence is we draw a white ball. So by Bayes' theorem, the probability of hypothesis 2 given the evidence is equal to the probability of the evidence given hypothesis 2 times the probability of hypothesis 2 divided by the probability of the evidence. Working through that, what you do is you come up with a probability of 0.0001. So the probability of hypothesis 2 given the evidence, therefore, that's the probability of evidence, I mean. The probability of the evidence is 0.001.

[01:11:57]  Unidentified speaker: That makes sense.

[01:11:57]  Bruce: There was only a 0.001 percent chance of pulling a white ball because that would require it to be a magic trick.

[01:12:04]  Unidentified speaker: Here's the problem though.

[01:12:05]  Bruce: We can now say, what is the probability of hypothesis 2 given the evidence? Well, that's going to be 1 times 0.0001 divided by 0.0001, which is 1. So the Bayesian is now certain, this is a magic trick according to the new model. But wait, where did the rule go that we can't have a 0 or 1 for a probability? Of course, we have to because Bayesian reasoning requires those as valid, okay? So this whole thing, we just collapsed this whole thing to be exactly equivalent to Popperian falsification.

[01:12:43]  Unidentified speaker: Why?

[01:12:44]  Bruce: Because what we really did is when you pull the white ball under this new model, where there's a small chance that it's a magic trick, the white ball falsifies hypothesis 1, and hypothesis 2 is now the only standing hypothesis. Therefore, the probability of hypothesis 2 is 1.0, okay? This is exactly equivalent to Popper's falsification at this point, okay? There is no difference than just saying I falsified that theory and now I'm going with the idea that it's a magic trick. The Bayesian epistemologist rule that you're never allowed to assign a probability of 0 makes no sense even within ordinary Bayesian reasoning. You can always justify it after the fact by adjusting the model, which is actually the right thing to do.

[01:13:33]  Unidentified speaker: Let me just say this.

[01:13:34]  Unidentified speaker: I'm only picking—

[01:13:35]  Bruce: I've tried to go through several different ways a Bayesian might try to resolve this, and I've shown that all of them have a problem. There are very sophisticated ways in which you could try to come up with a model to deal with this. I don't doubt you could get a very sophisticated model. You could keep expanding the model out. You could say, well, maybe there's a chance in my model that there's an error, even if there were three black balls, you could come up with some way to solve each individual problem I raise. It will always introduce a new problem when you do that, because when it comes right down to it, you're just doing the wrong thing. You really have to consider your model falsified. You can always justify it after the fact by adjusting the model, which is actually the right thing to do. But even that just pushes you back into accepting 0 and 1, as we just saw, as valid probabilities, which shows how entirely model dependent the analysis is.

[01:14:27]  Unidentified speaker: It still misses the deeper point.

[01:14:29]  Bruce: What you're really doing is a Popperian analysis with no probability assigned to the model itself.

[01:14:35]  Unidentified speaker: This makes sense.

[01:14:36]  Bruce: You can always rebuild the model to fit your new understanding. But that new model simply becomes the fresh set of assumptions your probabilities now depend on. To avoid that, you have to specify a model for every assumption in your model. If you wanted to avoid that problem, you would have to specify a model for every assumption in your model, and then a model for every assumption in that model, and so on. In short, you fall into the very same infinite regress that makes justificationism and induction impossible.

[01:15:07]  Unidentified speaker: And that's no coincidence.

[01:15:09]  Bruce: It's just another form of the very same problem. The key problem is that there's always infinitely many ad hoc theories to consider. And as per Cox's theorem, probability theory ceases to function when there are infinitely many theories to consider. But if you insist on including every possible theory, no matter how ad hoc, it is always the case you have infinitely many theories to consider. So yes, Solomonoff attempted to solve this problem via universal prior, which is a clever attempt to solve this problem. But as I've said, the universal prior, clever though it is, is incomputable, so it cannot save us here.

[01:15:46]  Unidentified speaker: Nor is it necessary.

[01:15:48]  Bruce: You can simply switch to Popperian epistemology and that solves the problem. All of this also resolves a puzzle that trips up many readers of Popper. In Popper's epistemology, you adopt the sole surviving theory as if it were true, but only tentatively.

[01:16:03]  Unidentified speaker: What does that even mean?

[01:16:04]  Unidentified speaker: It almost sounds like a contradiction on the face, doesn't it?

[01:16:07]  Bruce: To say, oh, I accept, wholly embrace this theory as true, but only tentatively. Like it sounds like a contradiction, but it isn't. Within a model, it makes perfect sense to adopt a theory that has survived, the only theory that has survived. Accepting a known inferior theory would be irrational, and it would make no sense to partially adopt the surviving theory, the sole surviving theory.

[01:16:32]  Unidentified speaker: That would mean giving some weight to an inferior theory at the same time, which would be irrational.

[01:16:37]  Unidentified speaker: So embracing the sole surviving theory as if it were true, setting its in-model probability to 1 is simply a rational move within the model.

[01:16:48]  Unidentified speaker: And yet, you know the model itself could be wrong.

[01:16:52]  Bruce: You just don't know where or how. In short, you assign a surviving theory, a probability of 1 within your current model, while staying open to revising the model entirely. That's all tentatively adopting as true means. This is, by the way, a great example of where Bayesian reasoning can help clarify critical rationalism. I just gave you a Bayesian understanding, a Bayesian reasoning understanding of what critical rationalists are doing.

[01:17:22]  Unidentified speaker: The two fold well into each other.

[01:17:24]  Bruce: By the two, I mean Bayesian reasoning, not Bayesian epistemology, which is wrong. Bayesian reasoning and critical rationalism are entirely compatible.

[01:17:34]  Unidentified speaker: Okay?

[01:17:35]  Unidentified speaker: They go together well.

[01:17:38]  Unidentified speaker: Now, thus, E. T.

[01:17:39]  Bruce: Jaynes, the father of Bayesian epistemology, says, quote, It is not the absolute status of a hypothesis embedded in the universe of all conceivable theories, but the plausibility of a hypothesis relative to a definitive set of specified alternatives that Bayesian inference determines. A hypothesis can attain a very high or very low probability within a class of well-defined alternatives. Its probability within the class of all conceivable theories is neither large nor small. It is simply undefined because the class of all conceivable theories is undefined. In other words, Bayesian inference deals with determined problems and we would not have it otherwise. That's from page 310 of Probability Theory, The Logic of Science by E. T.

[01:18:32]  Unidentified speaker: Jaynes.

[01:18:33]  Bruce: Now, this is shocking in how Popperian this statement actually is. By the way, in this section, he's railing on Popper, but he doesn't realize how Popperian he's being because he doesn't understand Popper, okay? For one thing, Jaynes is clearly agreeing with me that probability theory never gives you an absolute probability, but instead just gives you the relative strength of each theory in a defined list of proposed theories. Thus, it is, as I'm saying, always model dependent.

[01:19:03]  Unidentified speaker: Jaynes is agreeing with me.

[01:19:05]  Unidentified speaker: I got this from Jaynes.

[01:19:07]  Bruce: I never understood this until I read Jaynes' book.

[01:19:12]  Unidentified speaker: But he goes further.

[01:19:14]  Bruce: He's also claiming Bayesian inference only deals with specific determinant problems. Boy, does that sound suspiciously Popperian to you like it does to me?

[01:19:27]  Unidentified speaker: Jaynes is spot on here.

[01:19:29]  Unidentified speaker: Honestly, this quote I just read, it's completely right.

[01:19:32]  Unidentified speaker: It only gets one thing wrong.

[01:19:34]  Unidentified speaker: So not completely right.

[01:19:35]  Unidentified speaker: It gets one thing wrong.

[01:19:37]  Bruce: The one thing that this quote I just read, that he gets wrong, is his characterization of Bayesians. Because Bayesians today consistently try to work out absolute probabilities of their theories across every possible theory, exactly like Jaynes claims no good Bayesian should do. And that is what Bayesian epistemology is. In this section, Jaynes takes several pot shots at Popper, calling him and David Miller irrationalists.

[01:20:05]  Unidentified speaker: But let me keep quoting.

[01:20:07]  Bruce: You tell me if the Bayesianism of Jaynes isn't just a muddled version of critical rationalism. Now note for this next quote, I removed references to induction as a term from the quote. Critical rationalists have an allergy to that word, and I don't want to distract them, so instead I'm going to call it probabilistic inference. Focus on what's being said, not what it's being called, okay?

[01:20:28]  Unidentified speaker: So quote, the objection from Popper is often stated in different terms.

[01:20:32]  Unidentified speaker: If a theory cannot attain a high absolute probability, that's where I get the term, assigned against all alternatives, then there is no way to prove that the conclusions from it will be right.

[01:20:44]  Unidentified speaker: But that quite misses the point.

[01:20:46]  Bruce: It is not the function of probabilistic inference to be right. And working scientists do not use it for that purpose, and could not if we wanted to. The functional use of probabilistic inference in science is not to tell us what predictions must be true, but rather what predictions are most strongly indicated by our present hypotheses and our present information.

[01:21:13]  Unidentified speaker: That's from page 310 again.

[01:21:15]  Bruce: So, Jaynes is arguing that a good Bayesian would never claim probabilistic inference can tell you how reliable or correct a theory's predictions are. In other words, Bayesian inference tells you nothing whatsoever, according to Jaynes, about whether a theory is actually correct, contrary to how it's commonly used by Bayesian epistemologists today. What it does tell you, given a finite set of theories determined independently of Bayesianism, and assuming your background knowledge is correct, which it may not be, what it tells you is, which theory fits the combination of background knowledge and current evidence the best, out of the currently available theories. Okay, but if that's true, how does Jaynes' view of Bayesianism actually differ from Popper's theory of falsificationism? Despite Jaynes' obvious hatred of Popper, he really, really hates Popper.

[01:22:09]  Unidentified speaker: I just have to tell you how much he does.

[01:22:11]  Bruce: It doesn't seem to me it differs at all. Jaynes' theory is simply a restricted, muddled version of Popper's falsificationism.

[01:22:18]  Unidentified speaker: Don't believe me?

[01:22:20]  Bruce: Let's have Jaynes speak for himself. Here he is explaining what amounts to Popper's own theory of corroboration. Quote, If predictions made by a theory are borne out by future observation, then we become more confident of the hypotheses that led to them. And if the predictions never fail in vast numbers of tests, we come eventually to call these hypotheses, quote, physical laws. From successful induction, we do not learn anything basically new. We only become more confident of what we already knew.

[01:22:55]  Unidentified speaker: Page 311.

[01:22:57]  Unidentified speaker: Holy crap!

[01:22:58]  Bruce: That's practically David Miller's view compared to this actual, real David Miller quote.

[01:23:03]  Unidentified speaker: We might put things this way.

[01:23:05]  Bruce: When a theory fails a test, we learn something, but end up knowing nothing, since what we knew, our theory has been eliminated. But when a theory passes a test, when that is to say it is corroborated, we learn nothing, since we already knew what the result of the test was going to be, but we continue to know something, mainly the theory. Now, I have concerns with that quote from Miller for a variety of reasons, but there's just no doubt that it is basically exactly what Jaynes just said. Some crit rats will want to argue here that Jaynes, against Jaynes' wording of, then we become more confident of the hypothesis when it's corroborated. But do critical rationalists really, really, really believe that severe testing does not at least increase our internal confidence in a theory compared to, say, before it has never been tested at all? It seems to me that we should not quibble over what terms we use here. A Popperian might reword Jaynes like so. Then we become more confident that the competing theories are falsified and only one theory remains. And I doubt anything, that would be completely valid, critical rationalist wording, and I doubt anything in Jaynes' intent changed at all at this point.

[01:24:19]  Unidentified speaker: Still not convinced?

[01:24:20]  Unidentified speaker: Okay.

[01:24:21]  Unidentified speaker: How about this quote from Jaynes?

[01:24:23]  Bruce: Quote, on the other hand, if the predictions prove wrong, then induction has served its real purpose. We have learned that our hypotheses are wrong or incomplete. And from the nature of the error, we have a clue as to how they might be improved.

[01:24:38]  Unidentified speaker: Page 313.

[01:24:40]  Unidentified speaker: Oh my gosh!

[01:24:41]  Unidentified speaker: That's falsificationism!

[01:24:44]  Bruce: The whole point of induction he's claiming, probabilistic inference, we should probably call it instead, is that if the predictions don't come out the way we were expecting, that falsifies the theory.

[01:24:57]  Unidentified speaker: That's...

[01:24:57]  Unidentified speaker: Jaynes is saying that's why we do it.

[01:24:59]  Unidentified speaker: That's what induction is all about.

[01:25:01]  Unidentified speaker: Okay?

[01:25:01]  Bruce: So Jaynes continues, quote, So those who criticize induction on the grounds that it might not be right could not be possibly more mistaken. As Harold Jeffreys explained long ago, induction is most valuable to a scientist just when it turns out to be wrong. Only then do we get new fundamental knowledge. Page 311.

[01:25:24]  Unidentified speaker: Boom!

[01:25:25]  Bruce: It's exactly what Miller just said. Do you still doubt that Jaynes was accidentally agreeing with Popper here? I just don't see a way around this. Correct Bayesian reasoning is fundamentally equivalent to Popper's falsification. Still not convinced this is Popperian epistemology in disguise? Still think Bayesian reasoning can give us absolute model-independent probability as a theory? Okay, how about this quote from Jaynes? For example, this is Jaynes now. For example, if you ask a scientist, how well did the Zilch experiment support the Wilson theory? You might get an answer like this. Well, if you had asked me last week, I would have said that the evidence supports the Wilson theory very handsomely. Zilch's experimental point lies much closer, points lie much closer to Wilson's predictions than to Watson's. But just yesterday, I learned that this fellow Wolfson had a new theory based on more plausible assumptions, and his curve goes right through the experimental points. So now I'm afraid I have to say that the Zilch experiment pretty well demolishes the Wilson theory. That's from page 135. Holy crap, Bayesian probabilities change the instant your model changes. In this case, simply introducing a new theory. Under the old model, before Wolfson's theory existed, Wilson's probability, quote unquote, was high, simply because its only competitor at the time was Watson's theory. But introduce a better theory, and instantly the probabilities change drastically to the point that Wilson's theory now being considered demolished, even though the evidence didn't change.

[01:27:07]  Unidentified speaker: The evidence did not change.

[01:27:09]  Bruce: The only thing that changed was a new theory was introduced, so it changed the model. This is precisely Popper's epistemology, an evolutionary struggle between existing currently known theories that must be rethought at any time a new theory is discovered. So in his own words, Jaynes reveals what he actually believes about science, and it maps almost perfectly onto Popper's epistemology. So first we saw probabilistic inference can never tell you a theory is right. It only tells you which of your current competing theories is currently best supported by the evidence, by which we really mean least falsified by the evidence. That's not induction, that's critical rationalism. Second, successful predictions teach you nothing fundamentally new. In Jaynes' own words, you only become more confident about what you already know. Popper and Miller said exactly this about corroboration. Third, science advances only when a theory is falsified. Jaynes himself says induction, quote, serves its real purpose, unquote, when it turns out to be wrong. Because only then do we get fundamental new knowledge. Popper couldn't have said it better. Fourth, probabilities are always relative to a finite set of competing theories. Introduce a new theory and all the probabilities instantly shift. As the Wolfson example shows, there is no such thing as the absolute probability of a theory, which is precisely Popper's point. Fifth, given that probability theory only works with a finite set of theories and only measures their success relative to each other, how is this in any way inductive?

[01:28:42]  Bruce: You literally have a set of theories and a set of evidence, and you eliminate the theories as they underperform. How is induction, which is this is what Bayes, Jaynes calls induction, how is it anything but deduction? In short, Bayes uses Bayesian—Jaynes uses Bayesian language to describe a fundamentally Popperian picture of science. He rails against Popper, but he's doing Popper. Of course he is, for Popper discovered the true epistemology. So where does this all leave poor Pascal? The real problem with Pascal's wager is that it assumes Dawkins isn't free to simply take There is no God as his starting model and reason from there. You can debate whether that's the right starting assumption.

[01:29:30]  Unidentified speaker: That would be a fair debate.

[01:29:31]  Bruce: But there's no Bayesian rule that forces you to entertain God's existence any more than there is a Bayesian rule forcing you to pay Pascal's mugger. Does this entirely refute Pascal's wager? At least in the form Pascal originally wrote it, yes, it does.

[01:29:48]  Unidentified speaker: It refutes Pascal's wager.

[01:29:50]  Bruce: But understanding model dependence actually reveals how to reformulate Pascal's wager into a stronger form. Now, this episode is already long, so I won't dig into what we might call Pascal's improved wager.

[01:30:03]  Unidentified speaker: I will save that for another day.

[01:30:06]  Bruce: In fact, interestingly, the first time I heard Pascal's wager was from an LDS friend that gave it to me in the improved form. So for years, I mistakenly thought the improved version of Pascal's wager was Pascal's original intent. For decades, probably, I didn't understand that Pascal's original wager was not the improved form. Now, what happened is Latter-day Saints don't believe in an eternal hell of suffering, which was fundamental to Pascal's original formulation. So they were forced to reformulate Pascal's wager to accommodate that problem. Now, in doing so, they accidentally made it model dependent and thus valid. But Pascal's improved wager, it's too much for me to explain in this particular episode. We've gone on too long. We're going to have to save it for another episode. But there is an improved version of Pascal's wager I want to lay out at some point.

[01:31:00]  Unidentified speaker: It's not what you think.

[01:31:01]  Unidentified speaker: Okay.

[01:31:02]  Bruce: It's not a straight replacement for Pascal's wager. It does not force you to believe in God in any way.

[01:31:07]  Unidentified speaker: Okay.

[01:31:08]  Bruce: But it's a very interesting reformulation of Pascal's wager that makes it model dependent and therefore gets things right in terms of Bayesian reasoning. So we're going to save that for another time though. And I am done with my take on Pascal's wager as of today.

[01:31:24]  Peter: Well, that I was very curious what direction you were going to take this today. And this has been pretty, pretty epic in its own way. I, I, there's this whole, this whole idea that what you say about Bayesianism and critical rationalism being really so similar, it just, what you're saying makes so much sense. It just seems so sensible, but it's so different than what everyone else believes. That it's just amazing to me to be on this podcast and have access to this unique take that is, I would never have come across this in a million years, but here I am on this podcast listening to you.

[01:32:17]  Unidentified speaker: Here's how I would say it.

[01:32:18]  Unidentified speaker: And this is what I've told Ivan.

[01:32:19]  Unidentified speaker: Ivan the Bayesian, by the way.

[01:32:21]  Bruce: Okay, he laughed when I said this, all right? So I would say Bayesian epistemology is a false form of Bayesian reasoning. It has Bayesian reasoning in it, which is correct, but it also has some additional assumptions which are incorrect, such as the rule that you never set probabilities to zero or one. Okay, that really screws Bayesian reasoning up in a variety of ways. If you try to go with that rule, okay? So I would say that Bayesian epistemology is a muddled version of Popper's epistemology. And insofar as it happens to match Popper's epistemology, which it often does, they reason correctly. And insofar as they don't happen to match Popper's epistemology, they reason poorly. And usually, the difference between those two is whether they're relying on one of their rules that's wrong or not, okay? If they don't rely on those rules, Bayesian reasoning collapses back to Popper's epistemology. At least, I don't want to say it collapses back to Popper's epistemology because Bayesian reasoning is not an epistemology. It's a tool that you use inside of epistemology the same way you would use logic. Okay, so there is no epistemology of deductive logic.

[01:33:31]  Unidentified speaker: That doesn't even make sense.

[01:33:33]  Unidentified speaker: That's like an incoherent set of words.

[01:33:35]  Bruce: Bayesian epistemology, Bayesian reasoning epistemology is an equally incoherent set of words. But if you are understanding how to use Bayesian reasoning correctly, which Jaynes often did because he really understood it well, then what you're doing is exactly equivalent to Popper's epistemology. Okay, any correct use of Bayesian reasoning is Popper's epistemology, period, end of story.

[01:34:01]  Unidentified speaker: Here's the thing that's interesting.

[01:34:03]  Bruce: Any correct use of Popper's epistemology, now the caveat, in choosing between theories is by definition Bayesian reasoning. Popper's epistemology is a larger concept than Bayesian reasoning because it also includes when you don't have to choose between theories. Therefore, Popper's epistemology is the superset and Bayesian reasoning is the subset. Okay, but they're not different from each other. They have a deep, profound relationship, okay? I realize that just isn't how people look at it. Bayesian epistemology gets some things wrong, and insofar as they're wrong, they're wrong. I don't know what else to say. One of the things I pointed out to Ivan is I would say, look, when you realize you have a wrong model, what you're really doing is you're switching to a different model.

[01:34:56]  Unidentified speaker: He's like, yeah, of course that's what we're doing.

[01:34:57]  Bruce: That's what a Bayesian epistemologist would do. I'd say, but the new theory didn't come from Bayesian epistemology. It came from doing Popper's epistemology. You're jumping out to the larger epistemology, which is Popper's. You're coming up with a new model, then you're taking the evidence and you're reapplying it to the new model. You have to see that you don't have it all. You're just a little slice of the true epistemology.

[01:35:21]  Unidentified speaker: You're a true slice.

[01:35:22]  Bruce: You're a true slice of the true epistemology, but you're just a slice. You're just one little part of it. OK, if you really want to see what's going on, you just have to do it. If you're a Bayesian and you're reasoning well, which they often do, OK, it's not like Bayesians are idiots, they often reason very well, you have to see that you're often jumping outside of your Bayesian reasoning framework. You're doing something, and then you're coming back inside the Bayesian reasoning framework to make your decision. That jump out, that's the Popperian in you. You may not realize it, you may be doing it intuitively, but you are in your core still Popperian, at least when you're reasoning well. And I think that's the way I would put it.

[01:36:03]  Unidentified speaker: Here's the other interesting thing.

[01:36:04]  Unidentified speaker: I didn't know this was what was going to happen.

[01:36:06]  Bruce: Like when I started studying, I felt, I will cover this in a future podcast, but when I first started looking into Bayesian reasoning, I started off with the crit-rat criticisms of it. And it was obvious to me that something was wrong with the crit-rat, the criticisms of it.

[01:36:23]  Unidentified speaker: This often happens.

[01:36:26]  Bruce: I didn't take that to mean Bayesian epistemology was correct, but I took it to mean that crit-rats weren't doing the work to actually understand Bayesian reasoning. So I started to realize I'm never going to get a straight answer out of a crit-rat as to what the actual difference is. I'm going to have to look into it myself. So I bought Jane's book and the quotes I just gave you. It was with great shock when I realized, holy crap, he's doing Popper's epistemology. He's railing on Popper in one hand and he's doing Popper's epistemology with the other hand. And that was what I started to realize these two have a really close relationship and we really shouldn't have the negative view of Bayesian reasoning. We critical rationalists should not have the negative view of Bayesian reasoning that we currently have of it.

[01:37:09]  Unidentified speaker: It doesn't make any sense.

[01:37:11]  Bruce: It's a far more useful tool for critical rationalists than they think it is. So that is my point of view at this point at least.

[01:37:22]  Unidentified speaker: Well, I love what you're doing here.

[01:37:24]  Peter: I'm completely on board with this. It is funny how oftentimes when you go back to the original sources of these ideas, they're not the dichotomies that people make them out to be in our tribalistic mindsets or whatever. I've been listening to some, this is kind of a unrelated or vaguely related point, but I've been listening to Edmund Burke, some of his stuff, the founder of modern conservatism. And if you compare him to the founder of modern liberalism, JS. Mill, it's really not even obvious to me that they actually disagree that much in their worldviews. So I don't know, maybe we need to do a podcast on that as well, break down this whole liberalism versus conservatism thing.

[01:38:27]  Bruce: So I actually think that's a really common thing that happens. So like, let's say you took Solomonoff, who believes in induction, and came up with a way to show induction worked.

[01:38:37]  Unidentified speaker: Yeah.

[01:38:38]  Bruce: In my view, what he came up with was Popper's falsificationism. And yet it's dressed in inductive terms. And I don't even mean that in a bad way. Like what he really did is he took the—the concept of induction, and he found a way to make them work.

[01:38:57]  Unidentified speaker: But now they're exactly equivalent to the concepts of—of Popper's epistemology, and the—the difference is how they're worded.

[01:39:09]  Unidentified speaker: That kind of makes sense.

[01:39:11]  Bruce: Popper—Popper said that you can actually take any theory and you can redo it in any set of concepts or words you want, right? Like they're just instrument, he argued it just instruments, et cetera. So it makes sense that if you're an inductivist and you're going to try to make your theory work, reality constrains you to what actually works, which is going to end up being very close to Popper's epistemology, which was what actually works, right? And because of this, you're going to see convergence of ideas. You can have people who think they're disagreeing as they error correct their theories, they word it differently.

[01:39:47]  Unidentified speaker: They conceptualize it differently.

[01:39:49]  Bruce: And they're really attached to those concepts and words. But underneath, their theories are starting to make exactly the same predictions, which make them the same theory. And I think that's what you're really talking about liberal versus conservatism. I mean, we're kind of, this is a weird period of time where I'm not sure I align well with anybody. But if you really look at Burkean conservatism and Mill's liberalism, I think you're right that they converge, right? It's, they're both trying to find correct answers. One's approaching it from a conservative standpoint, one's approaching it from a liberal standpoint. Inevitably, as long as they error correct, they may use different words and different ways of saying things, but they're going to converge towards the truth. And I think this is a very common thing that people secretly agree, but don't realize it. So I guess I'm agreeing with you on that.

[01:40:45]  Unidentified speaker: Okay.

[01:40:46]  Unidentified speaker: Well, I love it.

[01:40:47]  Peter: And thank you for this, Bruce.

[01:40:50]  Unidentified speaker: Right.

[01:40:51]  Unidentified speaker: Thank you.

[01:40:59]  Unidentified speaker: Hello again.

[01:41:00]  Peter: If you've made it this far, please consider giving us a nice rating on whatever platform you use, or even making a financial contribution through the link provided in the show notes. As you probably know, we are a podcast loosely tied together by the Popper-Deutsch Theory of Knowledge. We believe David Deutsch's Four Strands tie everything together. So we discuss science, knowledge, computation, politics, art, and especially the search for artificial general intelligence. Also, please consider connecting with Bruce on X at bnielson01. Also, please consider joining the Facebook group, The Many Worlds of David Deutsch, where Bruce and I first started connecting.

[01:41:43]  Unidentified speaker: Thank you.